Value is a price gap, not a prediction
A "value" bet is not a bet you think will win. It is a bet where the price is longer than the true chance of winning. Sharps do not chase winners — they chase mispriced odds, then let a large number of bets grind out a profit.
To spot value you need two numbers: the probability the odds imply, and your own honest estimate of the real probability. When your estimate is higher than the implied number, you have found value. When it is lower, the book has found value on you.
Turn American odds into an implied probability
Every price on the board is really a probability in disguise. For a positive (underdog) price, implied probability = 100 / (odds + 100). For a negative (favorite) price, implied probability = |odds| / (|odds| + 100).
Example: a team is priced at +150. Implied probability = 100 / (150 + 100) = 100 / 250 = 40%. So the market thinks this team wins about 40 times out of 100. If your model says the true chance is 45%, the book is paying you as if the team is worse than you believe it is — that is value.
Expected value puts a dollar figure on the edge
Expected value (EV) is the average profit or loss per bet if you could place the same bet thousands of times. For a bet that risks your stake to win a profit: EV = (chance of winning x profit) - (chance of losing x stake).
Example: you risk $100 at +150, so a win returns $150 profit. You believe the win probability is 45%. EV = (0.45 x $150) - (0.55 x $100) = $67.50 - $55.00 = +$12.50. A positive EV means that, priced this way, the bet makes money on average even though it loses more often than it wins.
The lesson: a bet can lose 55% of the time and still be sharp, as long as the price pays you enough for the times it hits. Value lives in the gap between price and truth, not in the win-loss record of any single night.